The ACT math section tests 45 questions in 50 minutes — and it does NOT give you a formula sheet. Every formula you need must already be in your head when you sit down on test day. With a national average math score of just 19.0 and only 29% of students meeting the college readiness benchmark, knowing your ACT math formulas cold is one of the fastest ways to gain an edge.
The ACT Math section gives you 45 multiple-choice questions and 50 minutes to answer them. That works out to roughly one minute and seven seconds per question — not much room for hesitation. Each question has four answer choices, a calculator is permitted for the entire section, but no ACT math formula sheet is provided. Every equation, identity, and property you need must come from memory.
| Content Area | % of Questions | Key Formulas | Typical Question Count |
|---|---|---|---|
| Pre-Algebra & Arithmetic | ~20% | Percent change, ratios, mean | ~9 |
| Algebra | ~25% | Slope, linear equations, quadratic formula | ~11 |
| Geometry | ~25% | Area, perimeter, Pythagorean theorem, volume | ~11 |
| Coordinate Geometry | ~15% | Distance, midpoint, circle equation | ~7 |
| Trigonometry | ~7% | SOHCAHTOA, identities | ~3 |
| Statistics & Probability | ~8% | Mean, probability, combinations | ~4 |
The national average ACT Math score for the class of 2024 was 19.0 out of 36, and only 29% of students met the College Readiness Benchmark for Mathematics — a score of 22, which indicates a 50% chance of earning a B or higher in college algebra. Students who took three or more years of math beyond Algebra I, Algebra II, and Geometry had a 44% college readiness rate, compared to just 9% for those who stopped at the standard sequence.
The takeaway is clear: formula knowledge directly translates into test performance. Many ACT math questions are straightforward if you know the right formula — but impossible to solve efficiently without it. Memorizing these formulas is one of the highest-return study activities you can do.
Algebra questions make up roughly 25% of the ACT Math section, making this one of the most heavily tested categories. These ACT algebra formulas are the foundation for coordinate geometry problems as well.
The slope formula and slope-intercept form appear on virtually every ACT. You need to be able to calculate slope between two points using m = (y₂ − y₁) / (x₂ − x₁) and recognize when an equation is in y = mx + b form, where m is the slope and b is the y-intercept.
The distance formula d = √((x₂−x₁)² + (y₂−y₁)²) finds the straight-line distance between two coordinate points, while the midpoint formula ((x₁+x₂)/2, (y₁+y₂)/2) finds the point exactly between them. Both show up frequently in coordinate geometry questions.
When you cannot factor a quadratic equation, the quadratic formula is your fallback: x = (−b ± √(b²−4ac)) / 2a. The discriminant (b²−4ac) also tells you how many real solutions exist — positive means two solutions, zero means one, and negative means none. The ACT typically tests quadratics that can be factored, but the formula guarantees you can solve any quadratic you encounter.
Key exponent rules to memorize: when multiplying same-base terms, add exponents (am · an = am+n). When dividing, subtract exponents. When raising a power to a power, multiply exponents. A negative exponent means the reciprocal (a−n = 1/an), and any base raised to zero equals 1.
Worked Example
Find the distance between the points (2, 3) and (6, 7).
| Category | Formula | What It Finds | Priority |
|---|---|---|---|
| Algebra | y = mx + b | Slope-intercept form of a line | Must Know |
| Algebra | m = (y₂ − y₁) / (x₂ − x₁) | Slope between two points | Must Know |
| Algebra | d = √((x₂−x₁)² + (y₂−y₁)²) | Distance between two points | Must Know |
| Algebra | x = (−b ± √(b²−4ac)) / 2a | Solutions to a quadratic equation | Must Know |
| Geometry | A = ½bh | Area of a triangle | Must Know |
| Geometry | a² + b² = c² | Pythagorean theorem | Must Know |
| Geometry | A = πr² | Area of a circle | Must Know |
| Geometry | C = 2πr | Circumference of a circle | Must Know |
| Geometry | V = πr²h | Volume of a cylinder | Must Know |
| Trig | sin θ = opp / hyp | Sine ratio (SOH) | Must Know |
| Trig | cos θ = adj / hyp | Cosine ratio (CAH) | Must Know |
| Trig | tan θ = opp / adj | Tangent ratio (TOA) | Must Know |
| Stats | Mean = Σ / n | Average of a data set | Must Know |
| Stats | P = desired / total | Probability of an event | Must Know |
| Stats | nCr = n! / (r!(n−r)!) | Number of combinations | Good to Know |
Geometry is the single largest formula category on the ACT, accounting for about 25% of questions plus additional coordinate geometry problems. Mastering these ACT geometry formulas gives you a significant scoring advantage.
You must know area formulas for the most common shapes. Rectangle area = length × width. Triangle area = ½ × base × height. Parallelogram area = base × height. Trapezoid area = ½ × (b₁ + b₂) × height. For perimeter, add all sides — the ACT rarely gives you a perimeter formula because it expects you to know this intuitively.
The Pythagorean theorem (a² + b² = c²) is one of the most frequently tested formulas on the entire ACT. It applies only to right triangles, where c is the hypotenuse. Common Pythagorean triples to recognize instantly: 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Recognizing these saves time versus calculating.
| Triangle Type | Angles | Side Ratios | How to Remember |
|---|---|---|---|
| 45-45-90 | 45°, 45°, 90° | x : x : x√2 | Equal legs, hypotenuse is leg × √2 |
| 30-60-90 | 30°, 60°, 90° | x : x√3 : 2x | Shortest side × 2 = hypotenuse, middle side = short × √3 |
Circle questions appear consistently on the ACT. The two core formulas are Area = πr² and Circumference = 2πr (or πd). For arc length, multiply the circumference by the fraction of the circle: arc length = (central angle / 360) × 2πr. Sector area follows the same logic: sector area = (central angle / 360) × πr².
Volume questions are less frequent but still appear. The key formulas are: rectangular solid V = lwh, cylinder V = πr²h, cone V = (1/3)πr²h, and sphere V = (4/3)πr³. Cylinder volume is the most commonly tested of these.
Worked Example
A right triangle has legs of length 5 and 12. Find the length of the hypotenuse.
Trigonometry makes up about 7% of ACT Math questions — roughly 3 questions per test. Many students skip trig entirely and hope for the best. That is a mistake. These ACT trigonometry formulas are straightforward to memorize, and getting even 2-3 extra trig questions right can boost your score by a full point.
SOHCAHTOA is a mnemonic for the three basic trigonometric ratios in a right triangle:
"Opposite" and "adjacent" are always relative to the angle you are working with — not to the triangle as a whole. The hypotenuse is always the longest side, directly across from the 90° angle.
The reciprocal trig functions flip the basic ratios: cosecant = 1/sin, secant = 1/cos, and cotangent = 1/tan. The most important identity to memorize is the Pythagorean identity: sin²θ + cos²θ = 1. Also know that tan θ = sin θ / cos θ. These relationships let you convert between trig functions when a problem requires it.
Worked Example
In a right triangle, the side opposite angle θ is 3 and the hypotenuse is 5. Find sin θ, cos θ, and tan θ.
Statistics and probability questions make up about 8% of the ACT Math section. These are often the most straightforward formula-based questions on the test — if you know the ACT math equations, you can solve them quickly and bank time for harder problems.
The mean (average) = sum of all values / number of values. The ACT frequently asks you to find a missing value given a target average, which requires rearranging this formula. Median is the middle value when numbers are arranged in order. For probability: P(event) = desired outcomes / total possible outcomes.
Permutations (order matters): n! / (n−r)!. Combinations (order does not matter): n! / (r!(n−r)!). A quick way to remember: if you are choosing a team (where positions don't matter), use combinations. If you are arranging people in a line (where order matters), use permutations.
The percent change formula is (new − old) / old × 100. This comes up in word problems about price changes, population growth, and measurement comparisons.
Worked Example
A student scores 78, 85, 92, 88, and 72 on five tests. What score does she need on the sixth test to have an average of 85?
Enter the number of questions you want to attempt (out of 45) and see how much time you get per question.
The ACT does not provide a formula sheet — so every formula for the ACT math section must live in your memory. Here is what actually works for long-term formula retention.
Not all formulas carry equal weight. Start with the "Must Know" formulas in the reference table above — these appear on virtually every ACT. Once those are automatic, layer in the "Good to Know" formulas. Students aiming for scores above 30 should eventually know all 30-35 formulas, but even memorizing the top 15 gives you coverage for most questions.
Spend 5-10 minutes daily reviewing formulas rather than cramming for hours once a week. Consistent daily practice over 4-6 weeks is far more effective for long-term retention. Use flashcards — physical or digital — and write each formula from memory on blank paper. If you cannot write a formula without looking, you do not know it well enough for test day.
Memorizing a formula is only half the battle. You also need to recognize when to use it. Practice with real ACT questions so you build the pattern recognition to match a problem type with its formula. The more problems you solve, the faster your formula recall becomes under timed pressure.